Keep in mind that before upgrading you need 1,000 hours of 121 time. So you would need to fly for the airlines or a couple of years before being legal to upgrade at all.
With that said, you have military time, albeit low time. I'm not sure if the LCCs or Majors give credit for military time or not, but I would look into those airlines first.
If you do come to the Regionals first, stay away from Mesa and Republic. Otherwise, pick one that allows you to live in base.